AI 中文总结
该研究在对称monoidal范畴中证明，保持结合代数结构与余乘法的Hopf代数余作用自动保持其余单位等结构，推广统一了量子群仅具经典对称性的相关结果。
AI 中文摘要
我们证明，若一个Hopf代数对另一个对象的余作用保持后者的结合代数结构与余乘法，则该余作用自动也保持余单位、对极以及张量交换映射，且实际上可通过仿射群概型的作用对偶的余作用，经由Hopf代数自同态分解。这推广并统一了Kasprzak等人、Budziński-Kasprzak以及Brannan等人关于量子群仅具有经典对称性的一系列结果。所述自动经典性源于：在弱箭头收缩不变性假设下，任意对称monoidal范畴内部的Hopf代数的对极、余单位及张量交换映射，均包含于由结合代数结构与余乘法生成的（非对称）monoidal子范畴中。
英文摘要
We prove that a coaction of a Hopf algebra on another preserving the latter's associative-algebra structure and comultiplication automatically also preserves the counit, antipode, and tensor-interchange map and in fact factors through the coaction dual to an action of an affine group scheme by Hopf-algebra automorphisms. This generalizes and unifies a number of results to the effect that quantum groups have only classical symmetries, due to Kasprzak et al., Budziński-Kasprzak and Brannan et al. The stated automatic classicality follows from the fact that the antipode, counit and tensorand-interchange of a Hopf algebra internal to any symmetric monoidal category are contained in the (non-symmetric) monoidal subcategory generated by the associative-algebra structure and the comultiplication, assuming a weak form of arrow-retraction invariance.
Commentsv2 adds Remarks 1.6 and Example 1.7 and makes other minor alterations; 9 pages + references
